Question: What is the inverse of the function $g(x)=5(x-2)$ ? $g^{-1}(x)=$
Explanation: Let's start by replacing $g(x)$ with $y$. $y=5(x-2)$ If a function contains the point $(a,b)$, the inverse of that function contains the point $(b,a)$. So if we swap the position of $x$ and $y$ in the equation, we get the inverse relationship. In this case, the function is $y=5(x-2)$, so the inverse relationship is $x=5(y-2)$. Solving this equation for $y$ will give us an expression for $g^{-1}(x)$. $\begin{aligned} x&=5(y-2)\\\\ \dfrac{1}{5}x&=y-2\\\\ \dfrac{1}{5}x+2&=y\\\\\\ \end{aligned}$ The inverse of the function is $g^{-1}(x)=\dfrac{1}{5}x+2$. [I saw someone solve this problem by originally solving for x. Were they wrong?]